Sebastian,
> I am currently experimenting with curl-conforming elements and their > application in electromagnetism. I am using the Nedelec element FE_Nedelec > and > I have difficulties to understand the output and some other features: > > 1. I realized that VectorTools::project only works if QGauss<dim>(p) with p > >= 2 is used. AssertNoZerosOnDiagonal fails in precondition_SSOR. If I am > using an FE_System<dim>(FE_Q<dim>(1), dim) as the base element, everything > is fine. I don't know if this qualifies as a bug. But there is no > indication in the documentation of certain requirements on the quadrature > applied. There is a statement, but you're right that it isn't quite clear. I've proposed this here: https://github.com/dealii/dealii/pull/7587 > 2. I tried to output the curl of the vector, A, to a vtk file and used a > class derived from DataPostprocessor<dim> as suggested above. The results > do not look very promising if I compare them with the output of an > analytic curl of A, see screenshots attached. However the output of the > potential itself works as expected. It's hard to see anything in these figures if you don't know what it represents :-) I looked at the code briefly and it looks correct (though I'm not sure about the sign of each entry of the curl.) Try this on a simple case first where you take a simple vector-valued function (say, one whose curl is a constant vector), project it onto the mesh, and then output both the vector potential and the curl. > 3. Because of the problem related to the output of the curl I tried to > compute some errors. The projection error of the function value itself is > converging pretty well. I have tried to compute the L2-error of curl(A_h) > - curl(A) where A_h is the discrete approximation of A and A is the exact > potential. The curl error is not converging if I am refining the mesh. But > I am not sure if there is a mistake in my computation of the > cellwise_error. Does the potential A_h itself converge at the correct order? If yes, then its curl should converge at one order less. But since it's a derived quantity, make sure first that the quantity from which it is derived (i.e., the primary variable A_h) converges correctly and with the correct order. If it does and the curl doesn't, then you know that the problem lies with the way you compute the curl, not the way you compute A_h. Best W. -- ------------------------------------------------------------------------ Wolfgang Bangerth email: [email protected] www: http://www.math.colostate.edu/~bangerth/ -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. For more options, visit https://groups.google.com/d/optout.
